Understanding Criegee chemistry has become one of the central topics in atmospheric studies recently. Ozonolysis of unsaturated hydrocarbons is believed to be an important pathway of secondary organic aerosol (SOA). However, the SOA formation mechanisms via Criegee chemistry are still poorly understood. Here, we systematically study the competition between HO2 and H2O2 reactions with CH2OO/anti-CH3CHOO in the oligomer formations. The calculated results show that oligomers having Criegee intermediates as the chain units are produced by the sequential addition of Criegee intermediates (CIs) to HO2 and H2O2 molecules. The addition reactions are predicted to be strongly exothermic, and the apparent activation barriers are estimated to be negative, suggesting that these reactions are feasible both thermochemically and dynamically. Compared to the barriers of 4CH(2)OO + HO2 and 4CH(2)OO + H2O2 reactions, it can be found that the first two CH2OO addition reactions in the former case are favored, while the last two CH2OO addition reactions in the latter case are preferable. A similar conclusion is also obtained from those of the 4anti-CH3CHOO + HO2/H2O2 systems. The mechanistic insights can motivate future experimental studies of the effect of longer-chain CIs on the formation of SOA, which plays an important role on air quality and climate change.